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arXiv · 2603.08041

A generalization of Kadell's orthogonality ex-conjecture

Zihao Huang·Wenlong Jiang·Yue Zhou
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Abstract

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson constant term identity. The non-zero part of Kadell's conjecture is a constant term identity indexed by a weak composition $v$. This conjecture was first proved by K\'{a}rolyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above constant term when all parts of the composition $v$ are distinct. In 2021, Zhou obtained a recursion for this constant term for an arbitrary composition $v$. In this paper, by categorizing the variables into two parts, we generalize Zhou's result.

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Zihao Huang, Wenlong Jiang, Yue Zhou. 2026-03-09. A generalization of Kadell's orthogonality ex-conjecture. https://arxiv.org/abs/2603.08041

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